Although a relativistic system (or gravity [1]}) with torsion remains to be identified in the real world, we note that geometric torsion has been found to be inherent in the hydrodynamics of many condensed matter systems, including elasticity, see e.g. [2]}, [3]}, [4]}, [5]}, [6]}, topological quantum Hall and paired systems [7]}, [8]}, [9]}, semimetals [10]}, [11]}, [12]}, [13]}, [14]}, crystalline insulators [15]}, [16]} and in general non-relativistic Newton-Cartan spacetimes [17]}, [18]}, [19]}. As an example of the difference and similarities of the two independent anomaly sources, we discuss the two anomalies in a rotating chiral (non-relativistic) \(p+ip\)  Weyl superfluid or superconductor with a normal component and vortex lattice with vorticity and low-energy effective torsion, respectively. This gapless system is not strictly relativistic [20]} but instead, at low-energies, described by spatially anisotropic Newton-Cartan geometry that identifies the origin of the effective torsionful quasiparticle geometry in terms of the more directly familiar independent hydrodynamic variables and symmetries. However, in the linear approximation, the low-energy theory satisfies effective (local) Lorentz invariance along the special anisotropy direction, therefore the ingredients for (relativistic) CVE and CTE can be applied if the rotation, vorticity and torsion are along this special axis.
